Question: First consider the expression for: Take the product of $-3$ and $x$ and add $7$. Now select the answer that matches the following: The sum of $7$ and the product of $-8$ and that expression.
Solution: Let's break this problem into smaller and easier pieces. What is the product of $-3$ and $x$ $-3 \times x = \color{orange}{-3x}$ What does adding $7$ to $-3x$ do? $-3x$ $ + 7$ What is the quantity of $-8$ times that expression $-8 \times (-3x + 7) = \color{orange}{-8(-3x+7)}$ What is the sum of $7$ and $\color{orange}{-8(-3x+7)}$ $-8(-3x+7)$ $ + 7$ So the entire expression we're considering can be written as $-8(-3x+7)+7$.